Answer :

(i) Let us assume A = {1, 2}

And, B = {1, {1, 2}, {3}}

So,

And,

∴

But,

Hence, the given statement is false

(ii) Let us assume, A {2}

B = {0, 2}

And, C = {1, {0, 2}, 3}

It is given in the question that,

∴

But,

Hence, the given statement is false

(iii) It is given in the question that,

Let us assume,

So,

And,

∴

Hence, the given statement is correct

(iv) It is given in the question that,

A ⊄ B

And, B ⊄ C

Let us now assume, A = {1, 2}

B = {0, 6, 8}

And, C = {0, 1, 2, 6, 9}

∴

Hence, the given statement is false

(v) It is given in the question that,

And, A ⊄ B

Let us now assume, A = {3, 5, 7}

And, B = {3, 4, 6}

As,

And,

∴

Hence, the given statement is false

(vi) It is given in the question that,

A ⊂ B

And, x ∉ B

Let us suppose, then we have:

But it is given in the question that, x ∉ B

∴ x ∉ A

Hence, the given statement is true

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